There are a number of applications where it is desirable to geolocate an electromagnetic signal of unknown origin. For example, a corporate IT department may need to locate the source of an unauthorized wireless access point which compromises their network's security.
Of course precisely defining an object's location requires specifying coordinates in three dimensions (e.g., longitude, latitude, and altitude). In the discussion to follow, for simplicity of explanation it is assumed that the third coordinate (i.e., altitude) is either known or is otherwise easily determined once the other two coordinates (e.g., latitude and longitude) are identified. Those skilled in the art will be able to extrapolate the discussion to follow to the case where all three coordinates are to be determined.
There are several known methods to locate a signal emitter using a plurality of distributed sensors, or receivers, which are spaced apart from each other. Among these methods are: Angle of Arrival (AOA), Time Difference of Arrival (TDOA), and Received Signal Strength (RSS).
In the AOA method, the angle of arrival of the signal from a signal emitter is measured with special directional antennas at each receiver. This information is combined to help locate the signal emitter using lines of bearing. A chief limitation of the AOA method is that it requires special directional antennas at each receiver.
The TDOA method, also known sometimes as multilateration or hyperbolic positioning, is a process of locating an emitter by accurately computing the time difference of arrival at three or more sensors of a signal emitted from an emitter to be located. In particular, if a signal is emitted from a signal emitter, it will arrive at slightly different times at two spatially separated sensor sites, the TDOA being due to the different distances to each sensor from the emitter. For given locations of the two sensors, there is a set of emitter locations that would give the same measurement of TDOA. Given two known sensor locations and a known TDOA between them, the locus of possible locations of the signal emitter lies on a hyperbola. As shown in FIG. 1A, the hyperbola is defined as the locations where the difference between distances to the two sensors is a constant, or, in this case:r1−r2=v(t1−t2).
With three or more sensors, multiple hyperbolas can be constructed from the TDOAs of different pairs of sensors. The location where the hyperbolas generated from the different sensor pairs intersect is the most likely location of the signal emitter. In practice, the sensors are time synchronized and the difference in the time of arrival of a signal from a signal emitter at a pair of sensors is measured.
FIG. 1B illustrates some principles of a TDOA method of locating an emitter 105 using three sensors 110, 120 and 130. Shown in FIG. 1B are three range-defined hyperbolas 302, 304 and 306 for the three sensor pairs 110/120, 110/130 and 120/130. The location where the hyperbolas 302, 304 and 306 from the three sensor pairs intersect, as shown in FIG. 1B, is the most likely location of the signal emitter 105. In general, at least three sensors are required for the TDOA method, but more than three sensors can be employed.
In the RSS method, the power of the received signal at each sensor is measured, and the signal strength information is processed to help locate the signal emitter. There are a few different emitter location procedures that employ RSS.
In a basic RSS procedure, the power of the signal received at each sensor is measured. By knowing the broadcast power of the emitter, P0, one can convert the received power level, P1, to a range using the idealized expression: P1=P0*r1−2. Other variants of this equation use statistical approaches to account for varieties in terrain. The range from each sensor defines a circle of probable locations for the emitter, centered at that receiver. Another form of RSS is a relative power measurement, used when the power level of the signal transmitted at the emitter is not known. In this approach the relative signal power is measured at a pair of two sensors, and the received power levels at the sensors are processed to determine a circle of probable locations for the emitter.
A more detailed explanation of principles employed in such an RSS method of locating a signal emitter will now be provided with respect to FIG. 2.
FIG. 2 illustrates a general case of an emitter 105 and two sensors 110 and 120 which each receives a signal from emitter 105 wherein a circle 202 of probable locations for emitter 105 is determined from a ratio the received signal powers at sensors 110 and 120.
In free space, the received power of a signal transmitted by emitter 105 decreases with the square of the distance from emitter 105.
                                          P            1                    =                                                    P                0                            ⁡                              (                                                      r                    0                                                        r                    1                                                  )                                      2                          ,                            (        1        )            
where r1 is the distance between emitter 105 and sensor 110, and 2 is the exponential rate at which the power decreases with distance. The emitter transmit power is P0, as measured at distance r0 from the emitter. Likewise the received power P2 at sensor 120 is:
                                          P            2                    =                                                    P                0                            ⁡                              (                                                      r                    0                                                        r                    2                                                  )                                      2                          ,                            (        2        )            where r2 is the distance between emitter 105 and sensor 120.
This leads to:
                                          P            1                                P            2                          =                              (                                          r                2                                            r                1                                      )                    2                                    (        3        )            
With a bit of manipulation this yields:
                                                        log              ⁡                              (                                  P                  1                                )                                      -                          log              ⁡                              (                                  P                  2                                )                                              2                =                                            r              2                                      r              1                                =                      const            =            α                                              (        4        )            
This method is sometimes referred to as Signal Attenuation Difference of Arrival (SADOA). It can be shown that this leads to the circle 202 (the so-called circle of Apollonius) of a given radius R and centered on a point X0, Y0 located on the line 201 defined by the two sensors 110 and 120. This relationship is illustrated in FIG. 2.
With at least three sensors (e.g., A, B & C), three such circles are generated from the corresponding three unique pairs of sensors (e.g., A/B, A/C & B/C), and the location of emitter 100 can be found where the three circles intercept.
Several error factors affect the accuracy of geolocation measurements made by the AOA, TDOA, and RSS techniques described above. These error factors may include:                Noise. In low Signal-to-noise ratio (SNR) situations, emitter location is more difficult to determine with a high degree of accuracy because measurements of signal power, time-difference-of-arrival, etc. are affected.        Timing and calibration errors. Although these errors are typically small compared to other errors described here, there is nevertheless a need for algorithms that are robust in instances where these errors are significant.        Co-channel interference. Signals from multiple emitters that overlap in time and frequency can lead to ambiguous results.        Multipath propagation. Reflections from multipath propagation can distort or obscure the true time difference of arrival, angle of arrival, or strength of a signal received at a sensor.        Blocked line-of-sight, or un-detected direct path (UDP), is a condition in which the main propagation path between the emitter and receiver is blocked.        
In contrast to the AOA, TDOA and basic RSS methods described above, there are other emitter location methods that employ correlations of signals from two or more time synchronized sensors. If sensor A and sensor B are time synchronized with each other, then components of the signal received at each sensor that are similar will add constructively, while uncorrelated components such as noise do not add. The cross correlation approach can detect signals below the noise floor through the processing gain of the correlation operation.
To illustrate the point, consider the two discrete valued signals, x(k) and y(k) received at time synchronized sensors A and B. The cross correlation of x(k) and y(k), Rxy, is defined by equation (5) below.
                                          R            xy                    ⁡                      [            n            ]                          =                              lim                          N              →              ∞                                ⁢                                    1              N                        ⁢                                          ∑                                  k                  =                  0                                                  N                  -                  1                                            ⁢                                                          ⁢                              x                *                                  [                  k                  ]                                ⁢                                  y                  ⁡                                      [                                          k                      +                      n                                        ]                                                                                                          (        5        )            
We represent x(k) as the sum of a scaled original emitted signal p(k) plus an unwanted noise term, nA(k). We represent y(k) as the sum of a scaled and delayed original signal p(k) plus a different noise term, nB(k). The delay between sensor A and sensor B is represented by δ. The noise terms originate from internally generated receiver noise, hence two receivers may have the same noise performance, same noise statistics, and even the same root cause (e.g. thermal), but the noise signals themselves will be uncorrelated. This is illustrated in Equation (6).x[k]=A·p(k)+nA(k)y[k]=B·p(k−δ)+nB(k)  (6)
Substituting equation (6) into equation (5) yields equation (7).
                                          R            xy                    ⁡                      [            n            ]                          =                              lim                          N              →              ∞                                ⁢                                    1              N                        ⁡                          [                                                                    ∑                                          k                      =                      0                                                              N                      -                      1                                                        ⁢                                                                          ⁢                                                                                    ABp                        *                                            ⁡                                              (                        k                        )                                                              ⁢                                          p                      ⁡                                              (                                                  k                          -                          δ                          +                          n                                                )                                                                                            +                                                                            Ap                      *                                        ⁡                                          (                      k                      )                                                        ⁢                                                            n                      B                                        ⁡                                          (                                              k                        +                        n                                            )                                                                      +                                                      Bp                    ⁡                                          (                                              k                        -                        δ                        +                        n                                            )                                                        ⁢                                                            n                      A                      *                                        ⁡                                          (                      k                      )                                                                      +                                                                            n                      A                      *                                        ⁡                                          (                      k                      )                                                        ⁢                                                            n                      B                                        ⁡                                          (                      k                      )                                                                                  ]                                                          (        7        )            
According to equation (7), Rxy peaks when n equals δ, which is when the cross correlation lag is equal to the delay between sensor A and sensor B. If we allow that both noise terms are uncorrelated, and that the signal, p(k), is uncorrelated with noise, then the last three terms of the expression tend to diminish relative to the first term with increasing N. In other words, the longer a signal is observed, the more likely it is that it can be separated from the noise.
One example of a method which employs cross correlating the captured signal at different sensors or receivers is the Time Difference of Arrival from Cross Correlation method.
In many cases, the time-difference of arrival of a signal at two sensors is difficult to measure since the timing and signal characteristics of the emitter are unknown. In those cases, cross-correlation is a common method for determining the delay T. FIG. 1C shows an example cross-correlation curve 310. The time-difference of arrival between the two sensors is estimated as the location 312 where the curve 310 has its maximum. In practice, the cross-correlation curve is more complex and contains multiple features. These features may be pertinent to more sophisticated geolocation algorithms whose description is outside the scope of this application.
Meanwhile, U.S. patent application Ser. No. 12/325,708 filed on 1 Dec. 2008 describes a method and system for locating signal emitters using cross-correlations of received signal strengths (RSS) between pairs of sensors, and more specifically, ratios of cross-correlations of signal magnitudes from pairs of sensors including a common sensor in each pair. U.S. patent application Ser. No. 12/325,708 is incorporated herein by reference in its entirety for all purposes as if fully set forth herein.
However, there are some issues with these systems that use cross-correlations of the received signals. First, the cross correlation peak of two signals with significant multipath, noise, and interference has more ambiguity in time difference and amplitude than the noise free and multipath free case. Multipath can cause multiple peaks or overlapping peaks in the cross correlation function. It can make the estimate of time difference ambiguous. It would be better to cross correlate the received signal with an exact replica of the original transmit signal. Unfortunately, the original transmit signal is often unknown and unavailable for cross-correlation. Second, time domain data acquired at each sensor must be shared with other sensors or with a central processor to generate the cross correlations between all sensor pairs. Unfortunately in some cases the communication bandwidth between sensors is limited, and therefore transmitting a full time record of the signal received at each sensor to a central controller and/or to other sensors for cross-correlation can take a prohibitively long time.
What is needed, therefore, is a method and system for locating signal emitters that addresses one or more of these issues.